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Qmechanic ♦
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Ricci Tensor is the contraction of the Riemann Tensor. Even if all the components of the Ricci Tensor is zero, that doesn't mean that the spacetime is flat. If all the components of the Riemann Tensor is zero, then only the curvature is zero. In order for the field equations to be linear, the contraction is necessary. But, the contraction also neglects some components of the Riemann Tensor. Does it mean that the full Riemann curvature is not represented in the field equations?

Ricci Tensor is the contraction of the Riemann Tensor. Even if all the components of the Ricci Tensor is zero, that doesn't mean that the spacetime is flat. If all the components of the Riemann Tensor is zero, then only the curvature is zero. In order for the field equations to be linear, the contraction is necessary. But, the contraction also neglects some components of the Riemann Tensor. Does it mean that the full curvature is not represented in the field equations?

Ricci Tensor is the contraction of the Riemann Tensor. Even if all the components of the Ricci Tensor is zero, that doesn't mean that the spacetime is flat. If all the components of the Riemann Tensor is zero, then only the curvature is zero. In order for the field equations to be linear, the contraction is necessary. But, the contraction also neglects some components of the Riemann Tensor. Does it mean that the full Riemann curvature is not represented in the field equations?

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user355398
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Confusion regarding Riemann Tensor and Ricci Tensor

Ricci Tensor is the contraction of the Riemann Tensor. Even if all the components of the Ricci Tensor is zero, that doesn't mean that the spacetime is flat. If all the components of the Riemann Tensor is zero, then only the curvature is zero. In order for the field equations to be linear, the contraction is necessary. But, the contraction also neglects some components of the Riemann Tensor. Does it mean that the full curvature is not represented in the field equations?